that specifies the expectation values of the Wilson lines associated with links in \(M\) . Quite remarkably, an appropriate generalization [1]} of this procedure furnishes the solution of the abelian Chern-Simons theory in a generic closed and oriented 3-manifold \(M\) . Indeed, when the first homology group \(H_1(M)\)  is not trivial, for each element of the torsion subgroup [2]} of \(H_1(M)\)  one can introduce a corresponding classical background connection. Then one needs to take the sum of the Schwinger-Dyson functionals that are computed in the presence of each background connection. Somehow, in the functional integration, the values of the curvature correspond to the local degrees of freedom —which do not depend on the topology of the manifold \(M\) — whereas the effects of topology are taken into account by the background connections.
